David Hilbert

David Hilbert was a German Mathematician who lived from the late
19th to mid 20th centuries C.E. Known mainly as a geometer,
Hilbert also made significant contributions to set theory and
logic. In 1891, he formally described a space filling curve,
which now bears his name.

This project, like the Sierpinski project,
does not really use much math, just mathematical structures.
This time, I took the source image, averaged over square
pixels, then replaced the pixels with copies of the first four
iterations of Hilbert's space filling curve. Again, I used a
Floyd-Steinberg based algorithm to diffuse the error.

The great thing about this picture, which
isn't readily apparent, is that the entire picture is one
solid curve starting at the bottom left corning, going through
a large, Hilbert curve-shaped, path, and ending at the bottom
right corner. This picture was never displayed at a show, but
it was a fun project.

I can provide higher resolution images on
request. Here is a detail of the Hilbert curve showing a
number of iterations: